In the 140 square degree area covered by eFEDS, we detected 542 candidate clusters and groups of galaxies, down to the flux limit of \(\sim 10^{-14}~{\rm erg}~{\rm s}^{-1}~{\rm cm}^{-2}\)  in the soft band (0.5–2 keV) within 1. The clusters are distributed in the redshift range \(z=\) [0.01, 1.3], with the median redshift \(z_{\rm median}=0.35\) . The contamination fraction of non-cluster sources in the sample, dominated by AGN misidentified as extended sources, is \(\sim ~1/5\) , obtained from simulations. After accounting for the contamination, we find a cluster density of \(\sim 3.2\)  per square degree at this depth, in agreement with the expectations in [1]}. Our simulations suggest that it is possible to obtain a sample with a purity of \(>\) 90% if a simple cut at \(\mathcal {L}_{\rm ext}>15\)  is applied. This further selection delivers a subsample of \(\sim 270\)  clusters. However we note that the sample volume is unavoidably reduced as the high-redshift tail of the sample will have a smaller extent, and therefore be more severely cut by a higher \(\mathcal {L}_{\rm ext}\)  threshold. Most of these high-redshift clusters, however, are real, and the simulations predict that a few more of them will be found among the point-source detected population. In a following paper (Bulbul et al., in prep.), we will present a detailed assessment of the contribution of unresolved clusters to the eFEDS point-sources catalog. Further improvement on the characterization of the high-redshift clusters will be obtained thanks to the recently completed SDSS-IV and SDSS-V spectroscopic follow-up campaign, that will be presented elsewhere (Ider-Chitham et al., in prep.). We also found that \(\sim 16\%\)  of the clusters can be matched with a counterpart in the published X-ray or SZ cluster catalogs, indicating that the majority of the clusters in the sample are detected through their ICM emission for the first time.
